Vol. 7, No. 1, 2019

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Homogenization of nonlinear inextensible pantographic structures by $\Gamma$-convergence

Jean-Jacques Alibert and Alessandro Della Corte

Vol. 7 (2019), No. 1, 1–24
DOI: 10.2140/memocs.2019.7.1
Abstract

We prove the Γ-convergence of a pantographic microstructured sheet with inextensible fibers to a 2D generalized continuum model. Large deformations considered as geometrical nonlinearities are taken into account, and the Γ-convergence argument is developed in terms of convergence of measure functionals. We also prove a relative compactness property for the sequence of discrete energy functionals.

Keywords
$\Gamma$-convergence, nonlinear elasticity, generalized continua, pantographic structures
Mathematical Subject Classification 2010
Primary: 46G10, 74B20, 74Q05
Milestones
Received: 4 April 2018
Revised: 1 October 2018
Accepted: 29 November 2018
Published: 22 April 2019

Communicated by Pierre Seppecher
Authors
Jean-Jacques Alibert
Institut de Mathématiques de Toulon
Université de Toulon
La Garde
France
Alessandro Della Corte
International Research Center for the Mathematics and Mechanics of Complex Systems
Università degli Studi dell’Aquila
L’Aquila
Italy